<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>0185-1101</journal-id>
<journal-title><![CDATA[Revista mexicana de astronomía y astrofísica]]></journal-title>
<abbrev-journal-title><![CDATA[Rev. mex. astron. astrofis]]></abbrev-journal-title>
<issn>0185-1101</issn>
<publisher>
<publisher-name><![CDATA[Universidad Nacional Autónoma de México, Instituto de Astronomía]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0185-11012017000200001</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[Elements of a Gravitational Lens by Assuming an Elliptical Galaxy Model]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Molina]]></surname>
<given-names><![CDATA[U. E.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Viloria]]></surname>
<given-names><![CDATA[P.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Steffanell]]></surname>
<given-names><![CDATA[I.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad del Atlántico Departamento de Física ]]></institution>
<addr-line><![CDATA[Barranquilla ]]></addr-line>
<country>Colombia</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Universidad de la Costa Departamento de Ciencias Naturales y Exactas ]]></institution>
<addr-line><![CDATA[Barranquilla ]]></addr-line>
<country>Colombia</country>
</aff>
<aff id="Af3">
<institution><![CDATA[,Universidad Libre Facultad de Ingeniería ]]></institution>
<addr-line><![CDATA[Barranquilla ]]></addr-line>
<country>Colombia</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>00</month>
<year>2017</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>00</month>
<year>2017</year>
</pub-date>
<volume>53</volume>
<numero>2</numero>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S0185-11012017000200001&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S0185-11012017000200001&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S0185-11012017000200001&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[ABSTRACT In this work we study elements for gravitational lenses per galaxies such as the equation of lens, deviation angle, deflection potential and time delay, modeling the distribution of the volumetric mass of the lens in elliptical form. The function of volumetric distribution of mass in the deflecting galaxy &#961; has a nucleus with radius a in its core, form-free parameter b (b &gt; a), and volumetric density in its nucleus &#961;  0 . Through the distribution of volumetric mass density &#961;, we initially find surface mass density &#931; (projected on plane of the lens), followed by elements of a gravitational lens which are completely general and expressed in terms of the geometric parameters a and b. These are related by the adimensional factor  n =    b  &#945;  &gt; 1. Results are applied to a galaxy-specific lens system to conduct an analysis based on the temporal delay between two images and to observe the conditions with which parameter n must comply.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[RESUMEN En éste trabajo se estudian algunos elementos para lentes gravitacionales por galaxias como son ecuación de la lente, ángulo de desviación, potencial de desviación y retardo temporal, modelando la distribución volumétrica de masa de la lente en forma elíptica. La función de distribución volumétrica de masa en la galaxia deflectora &#961;, contiene en su centro un núcleo de radio a, una densidad volumétrica en su núcleo &#961;  0 and un parámetro libre de forma b, (b &gt; a). Mediante la distribución de densidad volumétrica de masa se encuentran inicialmente la densidad superficial de masa &#931;, (proyectada en el plano de la lente), para después hallar los elementos de una lente gravitacional los cuales son totalmente generales y quedan en términos de los parámetros geométricos &#945; and b, que se han relacionado mediante un factor adimensional  n =    b  &#945;  &gt; 1. Los resultados encontrados se aplican a un sistema de lente por galaxia particular para hacer un análisis basado en el retardo temporal entre dos imágenes y ver las condiciones que debe cumplir el parámetro n.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[Gravitational lens]]></kwd>
<kwd lng="en"><![CDATA[the lens equation]]></kwd>
<kwd lng="en"><![CDATA[deflection angle]]></kwd>
<kwd lng="en"><![CDATA[deflecting potential]]></kwd>
<kwd lng="en"><![CDATA[time delay]]></kwd>
</kwd-group>
</article-meta>
</front><back>
<ref-list>
<ref id="B1">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Adler]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
<name>
<surname><![CDATA[Schiffer]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Bazin]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
</person-group>
<source><![CDATA[Introduction to General Relativity]]></source>
<year>1975</year>
<publisher-loc><![CDATA[New YorK ]]></publisher-loc>
<publisher-name><![CDATA[McGraw-Hill co]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B2">
<nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Bartelmann]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
</person-group>
<source><![CDATA[On Arcs and Omega]]></source>
<year>1997</year>
</nlm-citation>
</ref>
<ref id="B3">
<nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Biggs]]></surname>
<given-names><![CDATA[A. D.]]></given-names>
</name>
<name>
<surname><![CDATA[Browne]]></surname>
<given-names><![CDATA[I. W. A.]]></given-names>
</name>
<name>
<surname><![CDATA[Helbig]]></surname>
<given-names><![CDATA[P.]]></given-names>
</name>
<name>
<surname><![CDATA[Koopmans]]></surname>
<given-names><![CDATA[L. V. E.]]></given-names>
</name>
<name>
<surname><![CDATA[Wilkinson]]></surname>
<given-names><![CDATA[P. N.]]></given-names>
</name>
<name>
<surname><![CDATA[Perley]]></surname>
<given-names><![CDATA[R. A.]]></given-names>
</name>
</person-group>
<source><![CDATA[MNRAS]]></source>
<year>1999</year>
<volume>304</volume>
<page-range>349</page-range></nlm-citation>
</ref>
<ref id="B4">
<nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Boughn]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
<name>
<surname><![CDATA[Crittenden]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
</person-group>
<source><![CDATA[]]></source>
<year>2001</year>
</nlm-citation>
</ref>
<ref id="B5">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Brainerd]]></surname>
<given-names><![CDATA[T. G.]]></given-names>
</name>
<name>
<surname><![CDATA[Blandford]]></surname>
<given-names><![CDATA[R. D.]]></given-names>
</name>
<name>
<surname><![CDATA[Smail]]></surname>
<given-names><![CDATA[I.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Weak Gravitational Lensing by Galaxies]]></article-title>
<source><![CDATA[Apj]]></source>
<year>1996</year>
</nlm-citation>
</ref>
<ref id="B6">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Ciufolini]]></surname>
<given-names><![CDATA[I.]]></given-names>
</name>
<name>
<surname><![CDATA[Archibald]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
</person-group>
<source><![CDATA[Gravitation and Inertia]]></source>
<year>1995</year>
<publisher-loc><![CDATA[New Jersey ]]></publisher-loc>
<publisher-name><![CDATA[Princeton Series in Physics]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B7">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Cohen]]></surname>
<given-names><![CDATA[A. S.]]></given-names>
</name>
<name>
<surname><![CDATA[Hewitt]]></surname>
<given-names><![CDATA[J. N.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Further Investigation of the Time Delay, Magnification Ratios, and Variability in the Gravitational Lens 0218+357]]></article-title>
<source><![CDATA[Apj]]></source>
<year>2000</year>
</nlm-citation>
</ref>
<ref id="B8">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Dyer]]></surname>
<given-names><![CDATA[C. C.]]></given-names>
</name>
<name>
<surname><![CDATA[Roeder]]></surname>
<given-names><![CDATA[R. C.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[The Distance-Redshift Relation for Universes with some Intergalactic Medium]]></article-title>
<source><![CDATA[Apj]]></source>
<year>1973</year>
</nlm-citation>
</ref>
<ref id="B9">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Foster]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Nightingale]]></surname>
<given-names><![CDATA[J. D.]]></given-names>
</name>
</person-group>
<source><![CDATA[A Short Course in General Relativity]]></source>
<year>1994</year>
<publisher-loc><![CDATA[NY ]]></publisher-loc>
<publisher-name><![CDATA[Springer-Verlag]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B10">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Golse]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
<name>
<surname><![CDATA[Kneib]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Pseudo Elliptical NFW Lensing Mass Model: application to the NFW mass distribution]]></article-title>
<source><![CDATA[Astronomy Astrophysics]]></source>
<year>2002</year>
<volume>390</volume>
<page-range>821-7</page-range></nlm-citation>
</ref>
<ref id="B11">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Grogin]]></surname>
<given-names><![CDATA[N. A.]]></given-names>
</name>
<name>
<surname><![CDATA[Narayan]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[A New Model of the Gravitational Lens 0957+561 and a Limit on the Hubble Constant]]></article-title>
<source><![CDATA[Apj]]></source>
<year>1996</year>
</nlm-citation>
</ref>
<ref id="B12">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Hjorth]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Kneib]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Elliptical galaxies as gravitational lenses]]></article-title>
<source><![CDATA[P. Apj]]></source>
<year>1997</year>
</nlm-citation>
</ref>
<ref id="B13">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Kenion]]></surname>
<given-names><![CDATA[I. R.]]></given-names>
</name>
</person-group>
<source><![CDATA[General Relativity]]></source>
<year>1995</year>
<publisher-loc><![CDATA[NY ]]></publisher-loc>
<publisher-name><![CDATA[Oxford Univrsity Press Inc.]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B14">
<nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Kessler]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
</person-group>
<source><![CDATA[]]></source>
<year>2009</year>
</nlm-citation>
</ref>
<ref id="B15">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Kormann]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
<name>
<surname><![CDATA[Schneider]]></surname>
<given-names><![CDATA[P.]]></given-names>
</name>
<name>
<surname><![CDATA[Bartelmann]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Astron]]></article-title>
<source><![CDATA[Strophys]]></source>
<year>1994</year>
<page-range>284-99</page-range></nlm-citation>
</ref>
<ref id="B16">
<nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Meneghetti]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Bartelmann]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Moscardini]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
</person-group>
<source><![CDATA[]]></source>
<year>2002</year>
</nlm-citation>
</ref>
<ref id="B17">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Miranda]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
<name>
<surname><![CDATA[Molina]]></surname>
<given-names><![CDATA[U]]></given-names>
</name>
<name>
<surname><![CDATA[Viloria]]></surname>
<given-names><![CDATA[P.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Retardo temporal en las lentes por galaxias en el contexto de Reissner - Nordstrom]]></article-title>
<source><![CDATA[Revista Mexicana de Física]]></source>
<year>2014</year>
<volume>60</volume>
</nlm-citation>
</ref>
<ref id="B18">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Molina]]></surname>
<given-names><![CDATA[U]]></given-names>
</name>
<name>
<surname><![CDATA[Tejeiro]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Viloria]]></surname>
<given-names><![CDATA[P.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Modelo Elíptico a partir del tiempo de retardo observacional]]></article-title>
<source><![CDATA[Rev. Colombiana de Física]]></source>
<year>2006</year>
<volume>38</volume>
<numero>3</numero>
<issue>3</issue>
</nlm-citation>
</ref>
<ref id="B19">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Narayan]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
<name>
<surname><![CDATA[Bartelmann]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
</person-group>
<source><![CDATA[Lectures on Gravitacional Lensing]]></source>
<year>1997</year>
<publisher-name><![CDATA[Max Planck-Institut für Astrophisik]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B20">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Schneider]]></surname>
<given-names><![CDATA[P.]]></given-names>
</name>
<name>
<surname><![CDATA[Ehlers]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Falco]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
</person-group>
<source><![CDATA[Gravitacional lenses]]></source>
<year>1992</year>
<publisher-loc><![CDATA[NY ]]></publisher-loc>
<publisher-name><![CDATA[Springer- Verlag]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B21">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Schneider]]></surname>
<given-names><![CDATA[P.]]></given-names>
</name>
<name>
<surname><![CDATA[Kochanek]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
<name>
<surname><![CDATA[Wambsganss]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
</person-group>
<source><![CDATA[Gravitational Lensing: Strong, weak and micro]]></source>
<year>2006</year>
<publisher-loc><![CDATA[Berlin Heidelberg ]]></publisher-loc>
<publisher-name><![CDATA[Springer-Verlag]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B22">
<nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Spingola]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
<name>
<surname><![CDATA[Dallacasa]]></surname>
<given-names><![CDATA[D.]]></given-names>
</name>
<name>
<surname><![CDATA[Orienti]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Giroletti]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[McKean]]></surname>
<given-names><![CDATA[J. P.]]></given-names>
</name>
<name>
<surname><![CDATA[Cheung]]></surname>
<given-names><![CDATA[C.C.]]></given-names>
</name>
<name>
<surname><![CDATA[Hovatta]]></surname>
<given-names><![CDATA[T.]]></given-names>
</name>
<name>
<surname><![CDATA[Ciprini]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
<name>
<surname><![CDATA[Ammando]]></surname>
<given-names><![CDATA[F. D.]]></given-names>
</name>
<name>
<surname><![CDATA[Falco]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
<name>
<surname><![CDATA[Larsson]]></surname>
<given-names><![CDATA[S., W.]]></given-names>
</name>
<name>
<surname><![CDATA[Max- Moerbeck]]></surname>
<given-names><![CDATA[W.]]></given-names>
</name>
<name>
<surname><![CDATA[Ojha]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
<name>
<surname><![CDATA[Readhead]]></surname>
<given-names><![CDATA[A. C.]]></given-names>
</name>
<name>
<surname><![CDATA[Richards]]></surname>
<given-names><![CDATA[J. L.]]></given-names>
</name>
<name>
<surname><![CDATA[Scargle]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
</person-group>
<source><![CDATA[MNRAS]]></source>
<year>2015</year>
<page-range>19</page-range></nlm-citation>
</ref>
<ref id="B23">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Weinberg]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
</person-group>
<source><![CDATA[Gravitation and Comology]]></source>
<year>1972</year>
<publisher-loc><![CDATA[New York ]]></publisher-loc>
<publisher-name><![CDATA[Wiley]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B24">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Wucknitz]]></surname>
<given-names><![CDATA[O.]]></given-names>
</name>
<name>
<surname><![CDATA[Biggs]]></surname>
<given-names><![CDATA[A. D.]]></given-names>
</name>
<name>
<surname><![CDATA[Browne]]></surname>
<given-names><![CDATA[W. A.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Models for the lens and source of B0218+357: a LENSCLEAN approach to determine H0]]></article-title>
<source><![CDATA[Mon. Not. R. Astron. Soc.]]></source>
<year>2004</year>
<volume>349</volume>
<page-range>1430</page-range></nlm-citation>
</ref>
<ref id="B25">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Yang]]></surname>
<given-names><![CDATA[Xi]]></given-names>
</name>
<name>
<surname><![CDATA[Yu]]></surname>
<given-names><![CDATA[Hao-Ran]]></given-names>
</name>
<name>
<surname><![CDATA[Zhang]]></surname>
<given-names><![CDATA[Tong-Jie]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Constraining smoothness parameter and the DD relation of Dyer-Roeder equation with supernovae]]></article-title>
<source><![CDATA[Astrophys]]></source>
<year>2013</year>
</nlm-citation>
</ref>
</ref-list>
</back>
</article>
